Graph of Composite Covariant Relations Between Node Types

GDMP Version 4 presents a higher–order graph constructed not from physical quantities but from types of physical description used across modern theoretical physics.At this level, nodes represent ontological categories such as information, geometry, dynamics, topology, quantum state, gauge field, and topological order. Edges are not postulated but arise as compositions of already known covariant laws, including the Ryu–Takayanagi relation, Jacobson’s thermodynamic derivation of Einstein equations, relative entropy, Fisher information metric, and topological field theory relations (Chern–Simons, Wilson loops, BF theory).The key idea of the GDMP Version 4 is that many pairs of description types, traditionally treated as unrelated in physics, become connected through chains of established equations. These composite edges form a closed covariant graph representing the structural closure of known theoretical frameworks.This graph does not introduce new physical laws. Instead, it demonstrates that modern physics already contains the necessary relations to connect quantum theory, gravity, topology, and information theory within a single structural scheme.GDMP Version 4 therefore defines:GDMP as the closure of known covariant laws into a unified graph of description types.Non-trivial Routes in the GraphWhat makes the GDMP Version 4 graph physically meaningful are the non-trivial paths that connect domains usually considered independent.Examples of such routes include:Quantum state → Information → Geometry → DynamicsQ → I → G → DRelative entropy → Ryu–Takayanagi → JacobsonHere, the Einstein field equations emerge as a consequence of properties of a quantum state.Gauge field → Topology → Information → GeometryF → O → I → GChern–Simons / Wilson loops → Topological entanglement entropy → RTGauge fields influence spacetime geometry through topological order and entropy.Topology → Information → Quantum stateO → I → QTopological entanglement entropy → Relative entropyTopological order constrains admissible quantum states.Closed physical cycleQ → I → G → D → O → I → QThis loop shows that quantum theory, gravity, topology, and information are not separate layers but parts of a single closed descriptive structure.Criterion for New PhysicsIf a relation between two node types cannot be reproduced by compositions of the known covariant laws represented in this graph, this indicates the presence of genuinely new physics rather than reinterpretation of existing theory.This artifact accompanies the GDMP Version 4 framework by providing a formal structural representation of how established theories interrelate at the level of their descriptive foundations, highlighting deep connections that are present implicitly in modern physics but rarely visualized as a single coherent structure.